Dynamic stochastic general equilibrium (DSGE) models have become a widely used tool for policymakers. This paper modifies the global identification theory used for structural vector autoregressions, and applies it to DSGE models. We use this theory to check whether a DSGE model structure allows for unique estimates of structural shocks and their dynamic effects. The potential cost of a lack of identification for policy oriented models along that specific dimension is huge, as the same model can generate a number of contrasting yet theoretically and empirically justifiable recommendations. The problem and methodology are illustrated using a simple New Keynesian business cycle model.